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Mat. Sb. (N.S.), 1981, Volume 116(158), Number 4(12), Pages 483–501 (Mi msb2478)  

This article is cited in 28 scientific papers (total in 28 papers)

Invertibility of almost periodic $c$-continuous functional operators

V. E. Slyusarchuk


Abstract: Statements are proved about the invertibility of operators $\frac{d^m}{dt^m}+A$ ($m$ a positive integer) and $B$ acting in the space of bounded vector-valued functions on $(-\infty,\infty)$ and in the space of bounded vector-valued functions on a countable Abelian group, respectively.
Bibliography: 25 titles.

Full text: PDF file (1577 kB)
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English version:
Mathematics of the USSR-Sbornik, 1983, 44:4, 431–446

Bibliographic databases:

UDC: 517.948.35
MSC: Primary 47E05; Secondary 34A10, 43A60, 46E15
Received: 02.01.1979 and 28.01.1981

Citation: V. E. Slyusarchuk, “Invertibility of almost periodic $c$-continuous functional operators”, Mat. Sb. (N.S.), 116(158):4(12) (1981), 483–501; Math. USSR-Sb., 44:4 (1983), 431–446

Citation in format AMSBIB
\Bibitem{Sly81}
\by V.~E.~Slyusarchuk
\paper Invertibility of almost periodic $c$-continuous functional operators
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 4(12)
\pages 483--501
\mathnet{http://mi.mathnet.ru/msb2478}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=665850}
\zmath{https://zbmath.org/?q=an:0503.34012}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 4
\pages 431--446
\crossref{https://doi.org/10.1070/SM1983v044n04ABEH000976}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Kurbatov, “Invertibility of almost-periodic operators”, Funct. Anal. Appl., 19:3 (1985), 223–224  mathnet  crossref  mathscinet  zmath  isi
    2. V. E. Slyusarchuk, “Invertibility of nonautonomous functional-differential operators”, Math. USSR-Sb., 58:1 (1987), 83–100  mathnet  crossref  mathscinet  zmath
    3. V. G. Kurbatov, “On the invertibility of almost periodic operators”, Math. USSR-Sb., 67:2 (1990), 367–377  mathnet  crossref  mathscinet  zmath  isi
    4. Bong C., “On Some Conditions of Reversibility of C-Continuity Differential-Functional Operators”, Dokl. Akad. Nauk, 329:3 (1993), 278–280  mathnet  zmath  isi
    5. A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. E. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of the non-linear difference operator $(\mathscr Dx)(t)=x(t+1)-f(x(t))$ in the space of bounded continuous functions on the real axis”, Sb. Math., 192:4 (2001), 565–576  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Slyusarchuk V., “Necessary and Sufficient Conditions for Existence and Uniqueness of Bounded and Almost-Periodic Solutions of Nonlinear Differential Equations”, Acta Appl. Math., 65:1-3 (2001), 333–341  crossref  mathscinet  zmath  isi
    8. V. E. Slyusarchuk, “Necessary and Sufficient Conditions for the Lipschitzian Invertibility of the Nonlinear Differential Mapping $d/dt-f$ in the Spaces $L_p({\mathbb R},{\mathbb R})$, $1\le p\le\infty$”, Math. Notes, 73:6 (2003), 843–854  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Slyusarchuk V.Yu., “Invertibility of the Nonlinear Operator (Lx)(T) = H (X(T), Dx(T)/Dt) in the Space of Functions Bounded on the Axis”, Nonlinear Oscil., 11:3 (2008), 442–460  crossref  mathscinet  isi
    10. Slyusarchuk V.Yu., “Generalization of the Mukhamadiev Theorem on the Invertibility of Functional Operators in the Space of Bounded Functions”, Ukr. Math. J., 60:3 (2008), 462–480  crossref  mathscinet  zmath  isi
    11. V. E. Slyusarchuk, “Conditions for the invertibility of the nonlinear difference operator $(\mathscr Rx)(n)=H(x(n),x(n+1))$, $n\in\mathbb Z$, in the space of bounded number sequences”, Sb. Math., 200:2 (2009), 261–282  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Slyusarchuk V.Yu., “Method of Local Linear Approximation in the Theory of Bounded Solutions of Nonlinear Differential Equations”, Ukr. Math. J., 61:11 (2009), 1809–1829  crossref  mathscinet  zmath  isi
    13. Slyusarchuk V.Yu., “Method of Local Linear Approximation in the Theory of Bounded Solutions of Nonlinear Difference Equations”, Nonlinear Oscil., 12:3 (2009), 380–391  crossref  mathscinet  isi
    14. Perestyuk M.O. Slyusarchuk V.Yu., “Green-Samoilenko Operator in the Theory of Invariant Sets of Nonlinear Differential Equations”, Ukr. Math. J., 61:7 (2009), 1123–1136  crossref  mathscinet  zmath  isi
    15. Slyusarchuk V.Yu., “Conditions for the Existence and Uniqueness of Bounded Solutions of Nonlinear Differential Equations”, Ukr. Math. J., 61:2 (2009), 320–335  crossref  mathscinet  zmath  isi
    16. V. E. Slyusarchuk, “The method of local linear approximation in the theory of nonlinear functional-differential equations”, Sb. Math., 201:8 (2010), 1193–1215  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Slyusarchuk V.Yu., “Conditions for the Existence of Bounded Solutions of Nonlinear Differential and Functional Differential Equations”, Ukr. Math. J., 62:6 (2010), 970–981  crossref  mathscinet  zmath  isi
    18. V. E. Slyusarchuk, “Bounded and periodic solutions of nonlinear functional differential equations”, Sb. Math., 203:5 (2012), 743–767  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. Slyusarchuk V.Yu., “Method of Local Linear Approximation of Nonlinear Differential Operators by Weakly Regular Operators”, Ukr. Math. J., 63:12 (2012), 1916–1932  crossref  isi
    20. V. E. Slyusarchuk, “The study of nonlinear almost periodic differential equations without recourse to the $\mathscr H$-classes of these equations”, Sb. Math., 205:6 (2014), 892–911  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. V. E. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of non-linear differential-difference equations”, Izv. Math., 78:6 (2014), 1232–1243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. Slyusarchuk V.Yu., “Conditions For Almost Periodicity of Bounded Solutions of Nonlinear Differential Equations Unsolved With Respect To the Derivative”, Ukr. Math. J., 66:3 (2014), 432–442  crossref  isi
    23. V. E. Slyusarchuk, “Conditions for the Existence of Almost-Periodic Solutions of Nonlinear Difference Equations in Banach Space”, Math. Notes, 97:2 (2015), 268–274  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    24. Slyusarchuk V.Yu., “a Criterion For the Existence of Almost Periodic Solutions of Nonlinear Differential Equations With Impulsive Perturbation”, Ukr. Math. J., 67:6 (2015), 948–959  crossref  mathscinet  isi
    25. V. E. Slyusarchuk, “Almost-periodic solutions of discrete equations”, Izv. Math., 80:2 (2016), 403–416  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    26. V. E. Slyusarchuk, “Necessary and sufficient conditions for the existence and uniqueness of a bounded solution of the equation $\dfrac{dx(t)}{dt}=f(x(t)+h_1(t))+h_2(t)$”, Sb. Math., 208:2 (2017), 255–268  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    27. Slyusarchuk V.Yu., “Favard-Amerio Theory For Almost Periodic Functional-Differential Equations Without Using the a"i-Classes of These Equations”, Ukr. Math. J., 69:6 (2017), 916–932  crossref  isi
    28. V. E. Slyusarchuk, “To Favard's theory for functional equations”, Siberian Math. J., 58:1 (2017), 159–168  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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